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Square Sides (Posted on 2024-01-01) Difficulty: 3 of 5
Find the smallest right triangle with integer sides such that the hypotenuse is a square and the sum of the legs is also a square.

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

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I suspect ... | Comment 4 of 7 |
If the triangle has sides a,b,c
where c (hypotenuse) is the square of integer n
and a+b is the square of integer m:
a^2 + b^2 = n^4 
and a+b = m^2

I could not find any solutions; I suspect there are no integer solutions.

Putting "x^2 + y^2 = n^4 integers" into Wolfram Alpha finds only (0,0,0)

  Posted by Larry on 2024-01-02 08:26:29
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